A Characteristic Map for Symplectic Manifolds

Details A Characteristic Map for Symplectic Manifolds A Characteristic Map for Symplectic Manifolds

2008-01-22

arxiv.org/abs/0801.3446v1

Mathematics

Symplectic Geometry

20 pages

Scientific paper

We construct a local characteristic map to a symplectic manifold M via certain cohomology groups of Hamiltonian vector fields. For each p in M, the Leibniz cohomology of the Hamiltonian vector fields on R^{2n} maps to the Leibniz cohomology of all Hamiltonian vector fields on M. For a particular extension g_n of the symplectic Lie algebra, the Leibniz cohomology of g_n is shown to be an exterior algebra on the canonical symplectic two-form. The Leibniz homology of g_n then maps to the Leibniz homology of Hamiltonian vector fields on R^{2n}.

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